OFFSET
1,1
COMMENTS
The dodecahedral conjecture (proved in 1988 by Thomas C. Hales and Sean McLaughlin, see links) states that, in any packing of unit spheres in the Euclidean 3-space, every Voronoi cell has volume at least equal to this value.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Thomas C. Hales and Sean McLaughlin, A proof of the dodecahedral conjecture, arXiv:math/9811079 [math.MG], 2008.
Thomas C. Hales and Sean McLaughlin, The Dodecaheral Conjecture, Journal of the American Mathematical Society, Vol. 23, No. 2, April 2010, pp. 299-344.
Wikipedia, Dodecahedral conjecture.
Wikipedia, Regular dodecahedron.
FORMULA
EXAMPLE
5.55029102851551026907043211366183924073759821288...
MATHEMATICA
First[RealDigits[10*Sqrt[130 - 58*Sqrt[5]], 10, 100]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 19 2024
STATUS
approved